A two-dimensional ruin problem on the positive quadrant: Laplace transform and inversion

Florin Avram (1) , Martijn Pistorius , Zbigniew Palmowski (2)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 Mathematical Institute, University of Wroclaw

We consider an exit problem of a certain two-dimensional process from a cone, inspired by applications in insurance and queueing theory. One motivation is to study the joint ruin problem for two insurance companies (insurance/reinsurance), or for two branches of the same company, which divide between them both claims and premia in some specified proportions, the goal being to split the risk (in particular when the claims are big). Another motivation is to provide an ex- ample of a multi-dimensional ruin model admitting analytic solutions. Indeed, we succeed, in the particular case of exponential claims, to derive the Laplace transform of the perpetual ruin probabilities and subsequently to invert it.

Domaines: Probabilités [math.PR]

Florin Avram, Martijn Pistorius, Zbigniew Palmowski. A two-dimensional ruin problem on the positive quadrant: Laplace transform and inversion. 2006. ⟨hal-00220380⟩